Question

The pressure acting on 500 cubic meters of gas is reduced from 4 atm to 2 atm. If the temperature remains constant, what is the new volume?

Answer 1

`"V"_"new"="1000 m"^3`

Explanation:

We will use Boyle's law, which states that pressure and volume are inversely proportional at constant temperature. We can express this mathematically as:

`"P"_1"V"_1="P"_2"V"_2`

Here, we see that

`"P"_1="4 atm"`
`"P"_2="2 atm"`

`"V"_1="500 m"^3`
`"V"_2="unknown"`

We want to manipulate Boyle's law to solve for `"V"_2`:

`"V"_2=("P"_1"V"_1)/("P"_2)`

Plugging in what we know:

`"V"_2=("4 atm" * "500 m"^3)/("2 atm")`

`"V"_2=2 * "500 m"^3`

`"V"_2="1000 m"^3`

We can see that the volume increased from `"500 m"^3` to `"1000 m"^3`, so it doubled. This is paired with the pressure being halved, as should be the case in an inversely proportional relationship.